An infinite element theory

A technique for solution of plane problems in mathematical physics or mechanics is presented. The method was developed initially for elastic plate problems with transverse load concentrations but is here extended to other two-dimensional problems. Draw-down problems with a number of wells in a porous medium, heat-flow problems in a plate with a distributed source, and with discrete sinks, or membrane displacements under concentrated forces, are considered in particular.The technique is to treat the two-dimensional medium as infinite: each source or sink is treated separately and equilibrated by an auxiliary source function. Superposition allows the effects of the separate sources and sinks to be added. The residual effect of the auxiliary source, after superposition, is negligible so that the summed effects of the individual sources and sinks gives the required solution. The method is approximate but the error may be made arbitrarily small. It is simple and well suited to the class of problems above, and to either manual or computer based analyses. Examples of its use are given.